Commonly, strain wave gearings have a rigid internally toothed gear, a flexible externally toothed gear coaxially disposed on the inner side of the internally toothed gear, and a wave generator fitted to the inner side of the externally toothed gear. Flat strain wave gearings comprise a flexible externally toothed gear in which external teeth are formed in the external peripheral surface of a flexible cylinder. The flexible externally toothed gears of cup-shaped and top-hat-shaped strain wave gearings comprise a flexible cylindrical barrel part, a diaphragm extending radially from the rear end of the cylindrical barrel part, and external teeth formed in the external peripheral surface portion of the front-end-opening side of the cylindrical barrel part. In a typical strain wave gearing, the circular flexible externally toothed gear is made to flex into an ellipsoidal shape by the wave generator, and both major-axis-directional ends of the ellipsoidally flexed flexible externally toothed gear mesh with the rigid internally toothed gear.
Since its invention by C. W. Musser (Patent Document 1), the strain wave gearing has been contrived in a variety of inventions and designs by many researches including the present inventor, as well as Musser himself. There are even a variety of inventions related merely to the tooth profile of strain wave gearings. In Patent Document 2, the present inventor proposed using the basic tooth profile as an involute tooth profile, and in Patent Documents 3 and 4 proposed using a technique in which a rack is used to approximate the meshing of the teeth of a rigid internally toothed gear and a flexible externally toothed gear as a tooth-profile-designing method for deriving an addendum tooth profile of both gears, which have a large area of contact.
In the tooth portion of an ellipsoidally flexed flexible externally toothed gear of a cup-shaped or top-hat-shaped strain wave gearing, the amount of radial flexure increases along the tooth trace direction from the diaphragm side toward the front-end opening, substantially in proportion to the distance from the diaphragm. As the wave generator rotates, various portions of the tooth part of the flexible externally toothed gear repeatedly Ilex radially outward and inward. To date, sufficient consideration has not been given to reasonable methods for designing a tooth profile in a manner that takes into consideration such flexural action (coning) of the flexible externally toothed gear caused by the wave generator.
In Patent Document 5, the present inventor proposed a strain wave gearing comprising a tooth profile by which continuous meshing is possible, with consideration given to coning of the teeth. In the strain wave gearing proposed in Patent Document 5, an arbitrary axially perpendicular cross-section of the tooth trace direction of the flexible externally toothed gear is selected as a principal cross-section, and at major-axis positions of an ellipsoidal rim neutral line of the flexible externally toothed gear in the principal cross-section, the amount of flexure 2κmn (where κ is a flexure coefficient, m is the module, and n is a positive integer) with respect to a rim neutral circle prior to flexure is set so that the gear flexes in a non-deflection state of 2mn (κ=1).
Using rack meshing to approximate meshing of the flexible externally toothed gear and the rigid internally toothed gear, in axially perpendicular cross-sections at positions including the principal cross-section in the tooth trace direction of the flexible externally toothed gear, movement loci of the teeth of the flexible externally toothed gear with respect to the teeth of the rigid internally toothed gear as the wave generator rotates are derived, a first homothetic curve BC is derived by scaling down, by a ratio λ (λ<1) using a point B as the homothetic center, a curve segment extending from a point A of an apical part to the point B in the next bottom part in a non-deflection movement locus obtained in the principal cross-section, and this first homothetic curve BC is adopted as the basic tooth profile for the addendum of the rigid internally toothed gear.
Furthermore, a second homothetic curve is derived by scaling, by a ratio (1-λ)/λ using an end point C of the first homothetic curve BC as the homothetic center, of a curve obtained by 180 degree rotation of the first homothetic curve BC about the end point C, and this second homothetic curve is adopted as the basic tooth profile for the addendum of the flexible externally toothed gear.
Additionally, in the tooth profile of the flexible externally toothed gear, an addendum modification is applied to the tooth profile portions on both sides of the principal cross-section in the tooth trace direction, so that both negative-deflection-side movement loci, which are obtained in axially perpendicular cross-sections flexed to a negative deflection state (flexural coefficient κ<1) toward the diaphragm side from the principal cross-section, and positive-deflection-side movement loci, which are obtained in axially perpendicular cross-sections flexed to a positive deflection state (flexural coefficient κ>1) toward the front-end-opening side from the principal cross-section, describe curves tangent to the bottom part of the non-deflection movement locus in the principal cross-section.
In a strain wave gearing in which a tooth profile is formed in this manner, not only can continuous meshing be achieved over a wide range between the addendum tooth profiles of the external teeth and internal teeth in a principal cross-section of the two gears, but effective meshing between the addendum tooth profiles of the external teeth and internal teeth through the entire range of the tooth trace direction can be achieved as well. Consequently, greater torque can be transmitted in comparison to a conventional strain wave gearing in which meshing takes place over a narrow tooth trace range.